NCERT Solutions for Class 8 Maths Chapter 11: Mensuration - Exercise 11.4

1. Given a cylindrical tank, in which situation will you find the surface area and in which situation volume.

a. To find how much it can hold.

Ans: To find the capacity of any object we find the volume. Here, see that it is asked how much the cylindrical tank can hold. Thus, we will find the volume of the tank in this case.

b. Number of cement bags required to plaster it

Ans: The walls of the tank will be cemented. This situation deals with the surface area. So, we will find the surface area of the cylinder to find the number of cement bags required to plaster it.

c. To find the number of smaller tanks that can be filled with water from it.

Ans: To find the capacity of any object we find the volume. Here, see that it is asked to find the number of smaller tanks that can be filled from the water. Thus, we will find the volume of the tank in this case.

2. The diameter of the cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without  doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has the greater area.

Ans: The volume of a cylinder with height $h$, and radius $r$ is $V = \pi {r^2}h$.

The diameter of cylinder A is 7 cm. 

The radius of cylinder A will be $\dfrac{7}{2}$ cm.

The diameter of cylinder B is 14 cm.

The radius of cylinder B will be 7 cm.

$ \Rightarrow \dfrac{7}{2} < 7$

For instance, if the value of $r$ and $h$ is the same, then the cylinder with the greater radius will have greater area.

We can see that the radius of cylinder B is greater, so, the volume of cylinder B will be greater. Now, verify it by calculating the volume of both the cylinders.

Assume the volume of cylinder A be ${V_A}$.

$\Rightarrow {V_A} = \pi  \times \dfrac{7}{2} \times \dfrac{7}{2} \times 14$

$ \Rightarrow {V_A} = \dfrac{{22}}{7} \times \dfrac{7}{2} \times \dfrac{7}{2} \times 14$

$ \Rightarrow {V_A} = 11 \times 7 \times 7$

$ \Rightarrow {V_A} = 539{\text{ c}}{{\text{m}}^3} $

Assume the volume of cylinder A be ${V_B}$.

$\Rightarrow {V_B} = \pi  \times 7 \times 7 \times 7 $

$ \Rightarrow {V_B} = \dfrac{{22}}{7} \times 7 \times 7 \times 7$

$ \Rightarrow {V_B} = 22 \times 49$

$ \Rightarrow {V_B} = 1078{\text{ c}}{{\text{m}}^3}  $

$ \Rightarrow {V_B} > {V_A}$

Hence, the volume of cylinder B is greater.

Now, we measure the surface area of both the cylinders to find which cylinder has a greater area. The formula of surface area of the cylinder be $L = 2\pi r\left( {r + h} \right)$.

Let the surface of the cylinder A be ${L_A}$.

$\Rightarrow {L_A} = 2 \times \dfrac{{22}}{7} \times \dfrac{7}{2}\left( {\dfrac{7}{2} + 14} \right)$

$\Rightarrow {L_A} = 2 \times 11 \times \left( {\dfrac{{7 + 28}}{2}} \right)$

$\Rightarrow {L_A} = 2 \times 11 \times \left( {\dfrac{{35}}{2}} \right)$

$\Rightarrow {L_A} = 11 \times 35$

$\Rightarrow {L_A} = 385\,{\text{c}}{{\text{m}}^2}$

Let the surface of cylinder A be ${L_B}$.

$\Rightarrow {L_B} = 2 \times \dfrac{{22}}{7} \times 7 \times \left( {7 + 7} \right)$

$\Rightarrow {L_B} = 2 \times 22 \times 14$

$\Rightarrow {L_B} = 44 \times 14$

$\Rightarrow {L_B} = 616\,{\text{c}}{{\text{m}}^2} $

From the above calculations, ${L_{\text{B}}} > {L_{\text{A}}}$.

Hence, cylinder B has greater surface area than the surface area of cylinder A.

3. Find the height of a cuboid whose base area is 180 square cm and volume is 900 cubic cm?

Ans: The base of the cuboid is rectangular. Thus, the area of the base is a product of length and breadth.  Thus, $A = 180\,{\text{c}}{{\text{m}}^2}$.

The volume of the cuboid is $V = l \times b \times h$. We are given that the volume is 900 cubic cm. 

$\Rightarrow 900 = 180 \times {\text{height}} $

$\Rightarrow \dfrac{{900}}{{180}} = {\text{height}} $

$\Rightarrow 5 = {\text{height}} $ 

Hence, the required height is 5 cm.

4. A cuboid is of dimension $60{\text{cm}} \times 54{\text{cm}} \times 30{\text{cm}}$. How many small cubes with side 6 cm can be placed in the given cuboid?

Ans: The volume of the cuboid is $V = l \times b \times h$. 

$\Rightarrow {V_{{\text{cuboid}}}} = 60{\text{cm}} \times 54{\text{cm}} \times 30{\text{cm}} $

$\Rightarrow {V_{{\text{cuboid}}}} = 97200{\text{c}}{{\text{m}}^3} $ 

The cube has a side length of 6 cm. The volume of the cube is given by $V = {\left( {{\text{side}}} \right)^3}$.

$ \Rightarrow {V_{{\text{cube}}}} = {\left( 6 \right)^3} $

$\Rightarrow {V_{{\text{cube}}}} = 216\,{\text{c}}{{\text{m}}^3} $ 

Let the required number of cubes be $n$.

$\Rightarrow n = \dfrac{{{\text{volume of the cuboid}}}}{{{\text{volume of the cube}}}} $

$ \Rightarrow n = \dfrac{{{\text{97200}}}}{{{\text{216}}}} $

$\Rightarrow n = {\text{450}} $ 

Hence, the required number of cubes are 450.

5. Find the height of the cylinder whose volume is $1.54\,{{\text{m}}^3}$ and the diameter of the base is 140 cm?

Ans: The diameter is 140 cm.

The radius is half of the diameter.

$ \Rightarrow r = \dfrac{{140}}{2}{\text{cm}} $

$ \Rightarrow r = 70{\text{cm}} $ 

Convert cm into m.

$\Rightarrow r = \dfrac{{70}}{{100}}{\text{m}} $

$ \Rightarrow r = \dfrac{7}{{10}}{\text{m}} $ 

Now, we will find the volume of the cylinder using the formula, $V = \pi {r^2}h$. Here, we are given that the volume is $1.54$.

$ \Rightarrow 1.54 = \dfrac{{22}}{7} \times \dfrac{7}{{10}} \times \dfrac{7}{{10}} \times h $

$\Rightarrow 1.54 = 22 \times \dfrac{1}{{10}} \times \dfrac{7}{{10}} \times h $ 

Isolate the variable to one side and the rest of the numbers to the other.

$\Rightarrow h = \dfrac{{1.54 \times 10 \times 10}}{{22 \times 7}} $

$\Rightarrow h = 1\,{\text{m}} $ 

Hence, the height of the cylinder is 1 m.

6. A milk tank is in the form of cylinder whose radius is $1.5$ m and length is 7 m. find the quantity of milk in litres that can be sorted in the tank?

Ans: The radius, $r$ of the cylinder is $1.5$m.

The length, $h$ of the cylinder is 7m.

The volume of the cylinder is given by $V = \pi {r^2}h$.

$\Rightarrow V = \pi  \times {\left( {1.5} \right)^2} \times \left( 7 \right) $

$\Rightarrow V = \dfrac{{22}}{7} \times 1.5 \times 1.5 \times 7 $

$  \Rightarrow V = 22 \times 2.25 $

$\Rightarrow V = 49.5\,{{\text{m}}^3} $ 

Now, we know that, $1\,{{\text{m}}^3} = 1000\,{\text{L}}$. So, convert the volume into litre.

$\Rightarrow 49.5\,{{\text{m}}^3} = 49.5 \times 1000\,{\text{L}} $

$\Rightarrow 49.5\,{{\text{m}}^3} = 49500\,{\text{L}} $ 

Therefore, 49500 litre of milk can be stored in the cylindrical tank.

7. If each edge of the cube is double,

i. How many times will its surface area increase?

Ans: Let the edge of the cube be $l$. Let the initial surface area be ${S_1}$.

The initial surface area will be ${S_1} = 6{l^2}$.

When the edge of the cube is doubled, $l$ becomes $2l$.

Let the new surface area be ${S_2}$.

$ \Rightarrow {S_2} = 6{\left( {2l} \right)^2} $

$ \Rightarrow {S_2} = 6\left( {4l} \right) $  

Thus, the surface area will increase 4 times when the edge of the cube is doubled.

ii. How many times will its volume increase?

Ans: Let the edge of the cube be $l$. Let the initial volume be ${V_1}$.

The initial volume will be ${V_1} = {l^3}$.

When the edge of the cube is doubled, $l$ becomes $2l$.

Let the new surface area be ${V_2}$.

$\Rightarrow {V_2} = {\left( {2l} \right)^3} $

$\Rightarrow {V_2} = 8{l^3} $ 

Hence, the volume becomes 8 times of the original volume when the radius is doubled.

8. Water is pouring into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of the reservoir is 108 cubic m, find the number of hours it will take to fill the reservoir?

Ans: The volume of the reservoir is 108 ${{\text{m}}^{\text{3}}}$.

First, we will convert the volume into litres. We know that, $1\,{{\text{m}}^3} = 1000\,{\text{L}}$. 

$ \Rightarrow 108{{\text{m}}^3} = 108 \times 1000\,{\text{L}} $

$\Rightarrow 108{{\text{m}}^3} = 108000\,\,{\text{L}} $ 

The water is getting poured at the rate of 60 litre per minute.

The amount of water poured in 1 hour will be,

$ \Rightarrow 60 \times 60\,{\text{L = 3600}}\,{\text{L per hour}}$

Let $n$ be the number of hours.

We can get the number of hours by dividing the total volume of the reservoir by the amount of water being poured.

$\Rightarrow n = \dfrac{{108000}}{{3600}} $

$\Rightarrow n = 30\,{\text{hours}} $ 

Hence, 30 hours will be required to fill the reservoir.

NCERT Solutions for Class 8 Maths Chapter 11 Mensuration (Ex 11.4) Exercise 11.4

Opting for the NCERT solutions for Ex 11.4 Class 8 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 11.4 Class 8 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

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